On Some Properties of the Heisenberg Laplacian

M. E. Egwe

Department of Mathematics, Universty of Ibadan.

DOI: 10.4236/apm.2012.25051                

Abstract

Let IH_n be the (2n+1) -dimensional Heisenberg group and let L_α and be the sublaplacian and central element of the Lie algebra of IH_n respectively. Forα=0 denote by L₀=L the Heisenberg Laplacian and let K ∈Aut(IH_n) be a compact subgroup of Au-tomorphism of IH_n. In this paper, we give some properties of the Heisenberg Laplacian and prove that L and T generate the K-invariant universal enveloping algebra, U(h_n)^k of IH_n.

Keywords

Heisenberg Group; Heisenberg Laplacian; Factorization; Universal Enveloping Algebra; Solvability

Conflicts of Interest

The authors declare no conflicts of interest.

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